Many of the Dark Eldar have all but lost their pyschic abilities due to not using them for a really long time. Many of the Kabaalite clone-slaves halfborne would be prime targets for Khorne's influence.... especially the Incubi. As far as mutation... uh... no idea lol.
Dark Eldar haven't lost their psyker abilities. They keep them suppressed with mental techniques and drugs. Their latent abilities are part of the reason She Who Thirsts has such a hand hold on their souls. http://wh40k.lexicanum.com/wiki/Psyker "Dark Eldar The Dark Eldar are similar in nature to the Eldar, but have given up the use of psychic powers. They do use psychic objects, but any psyker found on Commorragh is usually treated with great caution and fear. Because of the nature of their city, the use of psychic powers is one of the few things forbidden in the city of Commorragh.[6] Shadowseers are a notable exception to this rule.[7]"
They've been stunted to the point of being inconsequential thou, the only psykic power your average DE has is the ability to feed off the suffering of others. Asides that, they're pretty worthless psykers. No warp lightning being cast anytime soon.
It is artificially stunted. Their race alone makes them potentially powerful psykers. But that's besides the point which was: they are psykers and Khorne wouldn't want anything to do with them.
Azariah Kyras was pledged to Khorne. I don't know why that's not in lexicannum, but the altars making him invulnerable, his quotes, the demons he summoned, iconography, ect. were all to Khorne - and he was the chief librarian to the Blood Ravens. Again, the Dark Eldar view's on pyskers are pretty similar to Khorne's. If you think about it, Khorne's doing the same thing the Dark Eldar are doing - being a Chaos God is essentially the epitome of psychic power, and he's willingly denying that element of himself due to.... reasons.
It's not in Lexicanum because it's not canon that he solely worshipped Khorne. He even invokes Slaanesh at one point after his fall. I don't know, the Dark Eldar already heavily worship Khaine so why would they turn to Khorne? If anything, a Dark Eldar sorcerer would worship Tzeentch. I'm sure Tzeentch finds their plots and eternal maneuvering amusing and as an added bonus, he doesn't hate the way you feed yourself.
Perhaps they realize Khaine is a shadow compared to Khorne's raw power. I know it's rare, but the occasional Eldar should be able to see past their famous ego. And why woulf Khorne accept their worship? Well maybe to deny Slaanesh its prize, maybe he has a tolerancd that don't use offensive warpcraft (a possibility of much debate) or maybe just doesn't care from where the blood spills or who spills it.
I had assumed that Eldar were just different than humanity. Instead of their consciousness slowly being corrupted by daemonic knowledge/influence like it is with humans/astartes, their debauchery/pride/whatever "gave birth" to one of the 4 chaos gods that then had a claim on all of their souls. I'm not sure I understand the path of damnation. Lexicanum doesn't actually say that it's the worship of a chaos deity. It could be, but I don't think that it would particularly make sense. Eldar culture seems to revolve entirely around on protecting themselves from Chaos. I know that the Path of the Outcast is to reject the culture, but I'm not sure that it means rejecting everything that you know to be true. The path of damnation sounds more like mental illness to me.
That powerful a Psyker would probably have been bought by Tzeeneth from the Great IT anyway. I doubt Magnus would like such a rival.
Why would they not have a few that reject conventional culture? Widespread, clearly not, probably in large part due to if an Eldar mentioned that they were dabbling in Chaos lore, they'd probably be murdered. Once they've taken the Path of the Outcast there's little to limit their personal progression except the baggage they take with them. It seems perfectly reasonable to me that if a god has claim on your soul and wants to see you suffer for all eternity that your best chance at salvation would be to seek another, equally or more powerful god to shield you from its clutches. It also seems within reason that an Eldar would think their own discipline and power would be sufficient for them to master the madness of chaos rather than succumb to it. As Chaos practitioners their arrogance may even serve as protection from true corruption(when your will is subverted by the madness) as their strong sense of self reflects in the warp. It's not like the Eldar are immune, they just have a highly regimented life that makes it hard for such ideas to take hold.